$A$ large cloud of size $5 \, km \times 5 \, km$ is hovering over the Earth at a height of $1 \, km$. Assuming the cloud and the Earth form a parallel plate capacitor with air as the dielectric,calculate the capacitance of the cloud-Earth system in $\mu F$.

One plate of a parallel plate capacitor is connected to a spring as shown in the figure. The area of each plate of the capacitor is $A$ and the distance between the plates is $d$,when the battery is not connected and the spring is unstretched. After connecting the battery,in the steady state the distance between the plates is $0.75 d$,then the force constant of the spring is

$A$ parallel-plate capacitor consists of a fixed plate and a movable plate that is allowed to slide in the direction parallel to the plates. Let $x$ be the distance of overlap,as shown in the figure. The separation between the plates is fixed. Assume that the plates are electrically isolated,so that their charges $\pm Q$ are constant. Force on the movable plate is proportional to

$A$ parallel plate capacitor is made up of a stair-like structure with a plate area $A$ for each stair, and the plates are separated by distances $b$, $3b$, and $5b$ as shown in the figure. The capacitance of the arrangement is $\frac{ x }{15} \frac{\varepsilon_{0} A }{ b }$. The value of $x$ is ............

Two parallel plates separated by a distance of $5\,mm$ are kept at a potential difference of $50\,V.$ $A$ particle of mass $10^{-15}\,kg$ and charge $10^{-11}\,C$ enters in it with a velocity $10^7\,m/s.$ The acceleration of the particle will be

If the plates of a parallel plate capacitor connected to a battery are moved close to each other,then
$A$. the charge stored in it,increases.
$B$. the energy stored in it,decreases.
$C$. its capacitance increases.
$D$. the ratio of charge to its potential remains the same.
$E$. the product of charge and voltage increases.
Choose the most appropriate answer from the options given below: